Abstract

Iterative-series solutions have been recently developed for the scattering of p-polarized waves by a grating and for three-dimensional surfaces. However, their numerical behavior has not been investigated. We study the scattering by both dielectric and metallic sinusoidal gratings. We show that this kind of solution yields an accurate and efficient solution in the dielectric case. This solution may also be applied in conical-diffraction problems. Although some resonances have been successfully studied, the algorithm diverges for low values of the amplitude–period ratio in the case of metallic gratings.

References

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Table 1

Comparison between the Iterative-Series Solution, the Rearranged Iterative-Series Solution, and the Rayleigh Fourier Solutiona

ISS

RISS

RFS

n = l

n = 4

n = 8

n = 4

n = 8

P = 9

ρ0

0.384 × 10−1

0.716 × 10−2

0.669 × 10−2

0.712 × 10−2

0.669 × 10−2

0.689 × 10−2

ρ−1

0.294 × 10−1

0.154 × 10−1

0.160 × 10−1

0.156 × 10−1

0.160 × 10−1

0.159 × 10−1

E

1.09

0.997

1.000

0.997

1.000

1.001

t(s)

0.05

0.72

9.17

5.52

13.06

38.18

an is the number of orders used in the series, and P is the number of orders retained in the truncation of the linear system in the RFS; t is the computation time, and E is the sum of the efficiencies. The parameters are ∊ = 2.25, h/λ = 0.125, d/λ = 1.

Tables (8)

Table 1

Comparison between the Iterative-Series Solution, the Rearranged Iterative-Series Solution, and the Rayleigh Fourier Solutiona

ISS

RISS

RFS

n = l

n = 4

n = 8

n = 4

n = 8

P = 9

ρ0

0.384 × 10−1

0.716 × 10−2

0.669 × 10−2

0.712 × 10−2

0.669 × 10−2

0.689 × 10−2

ρ−1

0.294 × 10−1

0.154 × 10−1

0.160 × 10−1

0.156 × 10−1

0.160 × 10−1

0.159 × 10−1

E

1.09

0.997

1.000

0.997

1.000

1.001

t(s)

0.05

0.72

9.17

5.52

13.06

38.18

an is the number of orders used in the series, and P is the number of orders retained in the truncation of the linear system in the RFS; t is the computation time, and E is the sum of the efficiencies. The parameters are ∊ = 2.25, h/λ = 0.125, d/λ = 1.